It has helped my riding immensely to do no-stirrup work... I had to stop for a while due to the pony I had at the time bucking me off EVERY SINGLE TIME I rode him bareback or stirrupless, but then I sold him and got Monty, who was lacking in topline and really uncomfortable to ride bareback (and I had saddle issues at the time and couldn't keep my position well enough without stirrups). I really struggled with sitting the trot, especially in my dressage saddle, and then I started riding bareback again once Monty's topline had built up, and discovered that I actually CAN sit the trot, stay with my horse when he's trotting his big ground-covering trot, and jump higher than 2' bareback and not fall off. I have issues trusting him in the canter bareback but that's due to some nasty falls I have had off him, and feeling more vulnerable bareback.
Bareback and no-stirrup work are amazing when done right. I think the trick is to make sure you're moving with your horse, not ahead, and not behind. Move as much as necessary but as little as possible, and above all make sure that your core is engaged, your legs are in contact with your horse but NOT SQUEEZING, and your back is relaxed. It's the most incredible feeling when you get it right. My boy lifts and swings through his back like you wouldn't believe when I'm riding bareback. I'm sure he does it in a saddle too but I don't feel it as much.